TOPIC 11:

ROOM ACOUSTICS
 Contents
● General requirements.
● Theory of sound path in a room.
● Reflection, echo, types of reflectors.
● Absorption, absorption coefficient, types of absorber.
● Reverberation - Calculation of reverberation time.
 Room Acoustics
● Acoustic – is used to describe the study of sound in
general
- is concerned with the control of sound.

● The general aim is to provide the best conditions for the

production and the reception of desirable sounds
ROOM ACOUSTIC – general
principles
● concerned with the control of sound in an
enclosed space to provide the best
conditions for the production and the
reception of desirable sound and to handle
unwanted sound
● e.g. the control of noise.
General requirement
1. An adequate level of sound evenly distributed to all
listeners in the room.
2. A rate of decay (reverberation time) is suitable for the
type of the room.
3. Background noise and external noise reduced to
acceptable levels.
4. Absence of echoes and similar acoustics defects such as;
long day echoes, flutter echoes, sound shadows,
distortion and sound concentration.
3 TYPES OF AUDITORIUM
1) Speech
● The overall requirement for the good
reception of speech is that the speech is
intelligible.
● This quality will depend upon the power
and the clarity of the sounds.
● Examples; conference halls, law courts,
theatres and lecture rooms.
3 TYPES OF AUDITORIUM
2) Music
● Music consists of a wide range of sound levels
and frequencies which must all be heard.
● Some desirable qualities of music depend on the
listener’s judgement and taste.
● These qualities are difficult to define but terms
that are used in music include fullness of tone,
definition of sounds, blend of sounds and balance
of sound.
● Examples; concert halls, opera houses, recording
studios and practice rooms.
3 TYPES OF AUDITORIUM
3 Multi-purpose
● There are some conflicts between the ideal
acoustic conditions for music and for speech.
● Compromises have to be made in the design
of auditoria for more than one purpose and the
relative importance of each activity decided
upon.
● Examples; school halls, and theatres.
THE CHARACTERISTICS OF SOUND
PATHS IN ROOMS
● The behavior of sound inside an enclosed space
can produce many effects.
● The basic mechanisms are the wave properties
of:
1. Reflection
2. Absorption
3. Transmission
4. Diffraction
REFLECTION
● Sound is reflected in the same way of light –
angle of reflection=angle 0f incidence of the
wave
● Reflectors used to distribute sound evenly in an
enclosure and to increase the overall sound
level by reinforcement of the sound waves.
PLANE REFLECTOR – single plane
Image

Reflector

Source
SECTION
CURVE SURFACES REFLECTOR
1) CONCAVE surfaces tend to focus sound.
2) CONVEX surfaces tend to disperse sound
CURVE REFLECTOR
Return from corner

Source Focusing by
concave
surface
Dispersion by
convex
surface PLAN
ABSORPTION
● Sound absorption is a reduction in the sound
energy reflected from a surface.
● Sound absorption is a major factor in producing
good room acoustics, especially when
controlling reverberation.
ABSORPTION COEFFICIENT
● A measure of the amount of sound absorption
provided by a particular type of surface.
● The amount of sound energy not reflected is
compared with the amount of sound energy
arriving at the surface.
ABSORPTION COEFFICIENT
● Absorption coefficient = Absorbed sound energy
Incident sound energy

● UNIT : none – its value is expressed as a ratio

● The perfect absorber has an absorption coefficient of 1.0

and an example of such an absorber is an open window.
● Different construction materials have different
coefficients.
 ABSORPTION COEFFICIENT
COMMON BUILDING MATERIALS
125 Hz 500 Hz 2000 Hz
Brickwork Plain 0.02 0.03 0.04
Clinker blocks Plain 0.02 0.06 0.05
Concrete Plain 0.02 0.02 0.05
Cork Tiles 19mm, solid backing 0.02 0.05 0.10
Carpet Thick pile 0.10 0.50 0.60
Curtains Medium weight, folded 0.10 0.40 0.50
Medium weight, straight 0.05 0.10 0.20
Fibreboard 13mm, solid backing 0.05 0.15 0.30
13mm, 25mm airspace 0.30 0.35 0.30
Glass 4mm, in window 0.30 0.10 0.07
Tiles, solid backing 0.01 0.01 0.02
Glass fibre 25mm slab 0.10 0.50 0.70
Hardboard On battens, 25mm airspace 0.20 0.15 0.10
Plaster Lime or plaster, solid backing 0.02 0.02 0.04
on laths/studs, airspace 0.30 0.10 0.04
Plaster tiles Unperforated, airspace 0.45 0.80 0.65
Polystyrene tiles Unperforated, airspace 0.05 0.40 0.20
Water Swimming pool 0.01 0.01 0.01
Wood blocks Solid floor 0.02 0.05 0.10
Wood boards On joists/battens 0.15 0.10 0.10
Wood wool 25mm slab, solid backing 0.10 0.40 0.60
25mm slab, airspace 0.10 0.60 0.60
Special items
Air Per m3 0.007
Audience Per person 0.21 0.46 0.51
TOTAL ABSORPTION
● The effective absorption of a particular surface depends on
the area as well as on the absorption coefficient of the
material.
● A measure of this total absorption is obtained by
multiplying the two factors together.
TOTAL ABSORPTION
Absorption of a surface =
Area of surface (m2) x Absorption coefficient of that surface
UNIT : m2 sabins or ‘absorption units’

sum of the absorptions provided by each surface in the room. It

is the sum of the products of all areas and their respective
absorption coefficients.

Total Absorption = Σ(Area x Absorption coefficient)

3 types of absorber
●Porous
●Panel
●cavity
POROUS ABSORBERS
●Cellular materials:
Eg: ??
● Porous materials:
Eg: ??
POROUS ABSORBERS
●Cellular materials:
Eg: Fiberglass, mineral wools
● Porous materials:
Eg:
(1) POROUS ABSORBERS
●Cellular materials:
Eg: Fiberglass, mineral wools
● Porous materials:
Eg: Acoustic tiles, acoustic
blankets, acoustic plaster
Wall

(2) PANEL ABSORBERS

Panel

Air gap

Panel absorber
(3) CAVITY ABSORBERS

Enclosed space Opening

Cavity absorber
REVERBERATION
Definition: Continuing presence of an
audible sound after the source of the
sound has been stopped

Caused: Rapid multiple reflections

between the surfaces of a room
Multiple reflections of reverberation

Listener

Source
Direct and reverberant sound

Direct
Source sound
The sound waves that cause
reverberation lose intensity as they are
absorbed at each reflection and if the
source of sound stops then the
reverberant sound level decays

Reverberation time
REVERBERATION TIME
Definition: the time taken for the sound to decay by 60 dB
from its original level
Sound stops
Sound levels (dB)

60 dB

Reverberation time

Time in seconds (s)

FACTORS FOR REVERBERATION
TIME
1. distance between the surfaces of the
room
2. absorption at the surfaces
3. frequency of the sound
IDEAL REVERBERATION TIME (RT)
For acceptable acoustical quality :
speech: less than 1 s (short RT)
music: longer than 1 s (long RT)

Q: Larger rooms = short or long RT ?

A: Larger rooms = long RT

CALCULATION OF RT
RT - depends on
1. the volume of an enclosure (distance)
2. the total surface area
3. the absorption coefficients of the surfaces.

Sabine’s formula:
assumes that the reverberant decay is continuous and it is
found to give reasonable predictions of reverberation time for
rooms without excessive absorption.
SABINE FORMULA
t = 0.16V
A
t = reverberation time (s)
V = volume of the room (m3)
A = total absorption of room surfaces (m2 sabins)
= Σ (area x absorption coefficient)
Consideration in RT calculations
1. Reverberation times cannot be directly added or
subtracted with one another – adjustments must be made
by addition or subtraction of absorption units.
2. A sketch of the enclosures with dimensions will help in
accurately identifying all surfaces and their areas.
3. Surfaces that are not seen do not usually provide
absorption – for example, floor covered by carpet.
4. It is advisable to tabulate all surfaces with their
respective areas and absorption.
WORKED EXAMPLE 1
A lecture hall with a volume of 1500 m3 has the
following surfaces areas and finishes and absorption
coefficients (500 Hz).
● Walls, plaster on brick - 400m2 (0.02)
● Floors, plastics tiles - 300m2 (0.05)
● Ceiling, plasterboard on battens - 300m2 (0.10)
● Occupants - 100 people (0.46)

Calculate the reverberation time at 500 Hz of this hall.

Step 1: Tabulate information & calculate
absorption units (Area x Absorption coefficient)

500 Hz
Surface Area Absorption Abs. units
coefficient (m2 sabins)
Walls 400 0.02
Ceiling
Floor
Occupants
Total absorption (A)
Step 1: Tabulate information & calculate
absorption units (Area x Absorption coefficient)

500 Hz
Surface Area Absorption Abs. units
coefficient (m2 sabins)
Walls 400 0.02 8
Ceiling 300 0.1 30
Floor 300 0.05 15
Occupants 100 0.46 46
Total absorption (A) 99
Step 2: Calculate using Sabine’s formula

t = 0.16V
A
Step 2: Calculate using Sabine’s formula

t = 0.16V
A
= 0.16 (1500) / 99
= 2.42 s

Answer:
The reverberation time for the lecture hall is 2.42s
WORKED EXAMPLE 2
New reverberation time required for the hall in WE
1 is 0.8 sec. Calculate the area of acoustic tiling
needed on the walls to achieve this reverberation
time (absorption coefficient of tiles = 0.8 at 500
Hz).
Step 1: Tabulate information & calculate
absorption units (Area x Absorption coefficient)
500 Hz
Surface Area Absorption Abs. units
coefficient (m2 sabins)
Tiles Y 0.80

Walls 400 - Y 0.02

Ceiling 300 0.10

Floor 300 0.05
Occupants 100 people 0.46 each

Total A
Step 1: Tabulate information & calculate
absorption units (Area x Absorption coefficient)
500 Hz
Surface Area Absorption Abs. units
coefficient (m2 sabins)
Tiles Y 0.80 0.8Y

Walls 400 - Y 0.02 0.02(400 – Y)

= 8 – 0.02Y
Ceiling 300 0.10 30
Floor 300 0.05 15
Occupants 100 people 0.46 each 46
30+15+46+8-0.0
2Y+0.8Y
Total A
=99+0.78Y
Step 2: Calculate using Sabine’s formula

t = 0.16V
A
Step 2: Calculate using Sabine’s formula
0.8 = 0.16 x 1500
99 + 0.78Y

0.78Y = 0.16 x 1500 - 99

0.8
= 300 – 99
Answer:
Y= 201 Area of acoustic tiles
0.78 needed for RT of 0.8s
Y = 257.69 m2 is 258 m2
Work Example 3:

● A hall has a volume of 6000m3 and a reverberation time of

1.8s. Calculate the amount of extra absorption required to
obtain a reverberation time of 1 s.